Modeling Using Cubic Regression
Copy the data set below into Excel:
x
-0.2
0.3
0.9
2.3
2.9
y
4.2
3.7
-0.98
-3.8
6.87
Create a scatterplot (y vs x) of the data in Excel and paste your graph
below:
Find a quadratic regression model ( y  ax 2  bx  c ) for the data and
report the model below. What is the value of r-squared for this model?

Find a cubic regression model ( y  ax 3  bx 2  cx  d ) for the data and
report the model below. What is the value of r-squared for this model?

Which model is a better fit for the data? How do you know?
Use the superior model to predict the value of y when x=0.
Modeling Using Cubic Regression
Real Estate The table shows the average price (in thousands of dollars) of a
house in the Northeastern U.S. for 1987 to 1995. Let t be the number of
years since 1987.
t
0
1
2
3
4
5
6
7
8
f(t)
140
149
159.6
159
155.9
169
162.9
169
180
Create a scatterplot (Average Home Price vs. Year) of the data in Excel and
paste your graph below:
Find a quadratic regression model ( y  ax 2  bx  c ) for the data and
report the model below. What is the value of r-squared for this model?

Find a cubic regression model ( y  ax 3  bx 2  cx  d ) for the data and
report the model below. What is the value of r-squared for this model?

Which model is a better fit for the data? How do you know?
Use the superior model to predict the price of a home in the year 2000.
Modeling Using Cubic Regression
Space Exploration The table shows the average speed y (in feet per
second) of a space shuttle for different times t (in seconds) after launch.
t
10
20
30
40
50
60
70
80
y
202.4
463.4
748.2
979.3
1186.3
1421.3
1795.4
2283.5
Create a scatterplot (Average Speed vs Time after Launch) of the data in
Excel and paste your graph below:
Find a quadratic regression model ( y  ax 2  bx  c ) for the data and
report the model below. What is the value of r-squared for this model?

Find a cubic regression model ( y  ax 3  bx 2  cx  d ) for the data and
report the model below. What is the value of r-squared for this model?

Which model is a better fit for the data? How do you know?
Use the superior model to determine the speed of the space shuttle 100
seconds after the launch.